The distribution of class numbers in a special family of real quadratic\n fields

2016/03/02 by Alexander Dahl, Dahl, Alexander, Youness Lamzouri +1
Mathematics · Social Sciences · #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Vietnamese History and Culture Studies

paper · pdf · doi:10.48550/arxiv.1603.00889

openalex publication_date 2016/03/02 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We investigate the distribution of class numbers in the family of real\nquadratic fields \ℚ(\√(d)) corresponding to fundamental\ndiscriminants of the form d=4m²+1, which we refer to as Chowla's family. Our\nresults show a strong similarity between the distribution of class numbers in\nthis family and that of class numbers of imaginary quadratic fields. As an\napplication of our results, we prove that the average order of the number of\nquadratic fields in Chowla's family with class number h is (\log h)/2G,\nwhere G is Catalan's constant. With minor modifications, one can obtain\nsimilar results for Yokoi's family of real quadratic fields\n\ℚ(\√(d)), which correspond to fundamental discriminants of the\nform d=m²+4.\n

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